Finite Group Databasebeta

← #34070249

Subgroups — #34070249

Order 19328.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012738C211yesmaximal, characteristic
2C2×#18012663C211yesmaximal, characteristic
3#23752119C211yesmaximal, characteristic
4#23751975C211yesmaximal, characteristic
5#23751974C211yesmaximal, characteristic
6#23751966C211yesmaximal, characteristic
7C2×#103×C151C211yesmaximal, characteristic
8C22×Dic302—21no—
9C22×C151⋊C8C2211yescharacteristic
10#18012738—22no—
11#18012738—22no—
12C2×C4⋊Dic151C2211yescharacteristic
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4—21no—
15C2×C4×Dic151C2211yescharacteristic
16#18012663—22no—
17C151⋊#95—21no—
18C151⋊#95—21no—
19C22×Q8×C151C2211yescharacteristic
20C22×C8×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22#103×C151—22no—
23C2×Dic302—24no—
24C2×Dic302—42no—
25C2×Dic302—42no—
26C22×Dic151—21no—
27C22×Dic151—21no—
28C22×Dic151D411yescharacteristic
29C22×Dic151D411yescharacteristic
30C2×C151⋊C8—21no—
31C2×C151⋊C8—21no—
32C2×C151⋊C8—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D412yes—
37Dic151⋊C4—24no—
38C4×Dic151—21no—
39C4×Dic151—21no—
40C2×Q8×C151—21no—
41C2×Q8×C151—21no—
42C2×Q8×C151—21no—
43C2×Q8×C151—21no—
44C2×Q8×C151—21no—
45C2×Q8×C151Q812yescomplemented
46C22×C4×C151—21no—
47C22×C4×C151—21no—
48C22×C4×C151C2311yescharacteristic
49C2×C8×C151—21no—
50C2×C8×C151—21no—
51C2×C8×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D412yes—
54Dic302—48no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—22no—
60C2×Dic151—41no—
61C2×Dic151—41no—
62C2×Dic151—41no—
63C2×Dic151—41no—
64C2×Dic151—41no—
65C2×Dic151SD1612yes—
66C2×Dic151Q1612yes—
67C151⋊C8—41no—
68C23×C151C2×D411yescharacteristic
69Q8×C151—22no—
70Q8×C151—22no—
71Q8×C151—41no—
72Q8×C151—41no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—41no—
76C2×C4×C151—41no—
77C2×C4×C151—41no—
78C2×C4×C151—41no—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×Q811yescharacteristic
82C2×C4×C151#4111yescharacteristic
83C2×C4×C151#4111yescharacteristic
84C2×C4×C151#4111yescharacteristic
85C8×C151—41no—
86C22×C151#12011yescharacteristic
87C22×C151C22⋊Q811yescharacteristic
88C22×C151#12411yescharacteristic
89C22×C151C2×SD1611yescharacteristic
90C22×C151C2×Q1611yescharacteristic
91C22×C151AGL(1,ℤ/8)11yescharacteristic
92C22×C151#13711yescharacteristic
93C4×C151—42no—
94C4×C151—42no—
95C4×C151C22⋊Q811yescharacteristic
96C4×C151C22⋊Q811yescharacteristic
97C4×C151#12411yescharacteristic
98C4×C151#12411yescharacteristic
99Dic151—22no—
100Dic151—22no—
101Dic151—42no—
102Dic151—81no—
103C2×C151#39311yescharacteristic
104C2×C151#45011yescharacteristic
105C2×C151#45111yescharacteristic
106C2×C151#47511yescharacteristic
107C2×C151#47711yescharacteristic
108C2×C151#48711yescharacteristic
109C2×C151#48911yescharacteristic
110C151#202411yescharacteristic, complemented, Sylow
111#2024—1511nomaximal, Sylow
112C2×C4⋊Q8—1511no—
113C2×#103—1511no—
114C2×#103D15111yescharacteristic
115#391—1511no—
116#340—1511no—
117#340—1511no—
118#336—1511no—
119C22×Q8—3021no—
120C22×Q8C2×D15111yescharacteristic
121C22×C8—1511no—
122C22×C8C2×D15111yescharacteristic
123C4⋊Q8—3022no—
124C4⋊Q8—3022no—
125C2×C4⋊C4—3021no—
126C2×C4⋊C4—1511no—
127C2×C4⋊C4—1511no—
128C2×C4⋊C4C2×D15111yescharacteristic
129C2×C42—1511no—
130#103—22no—
131#103—3022no—
132#95—3021no—
133#95—3021no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—3024no—
140C2×Q8—6042no—
141C2×Q8—6042no—
142C2×Q8Dic30212yescomplemented
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3021no—
146C22×C4—3021no—
147C22×C4—1511no—
148C22×C4—1511no—
149C22×C4C22×D15111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—3021no—
154C2×C8—3021no—
155C2×C8—3021no—
156C4⋊C4—21no—
157C4⋊C4—3024no—
158C4⋊C4—3021no—
159C4⋊C4—3021no—
160C4⋊C4—3021no—
161C4⋊C4—1512no—
162C4⋊C4C22⋊D15112yes—
163C42—3021no—
164C42—3021no—
165C23D4×D15111yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—6048no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3021no—
178C2×C4—3021no—
179C2×C4—3021no—
180C2×C4—3021no—
181C2×C4—3022no—
182C2×C4—6041no—
183C2×C4—6041no—
184C2×C4—6041no—
185C2×C4—6041no—
186C2×C4—6041no—
187C2×C4—1512no—
188C2×C4—1512no—
189C2×C4D4×D15111yescharacteristic
190C2×C4C2×C22⋊D15111yescharacteristic
191C2×C4C2×Dic30211yescharacteristic
192C2×C4#1455900311yescharacteristic
193C2×C4#1455900311yescharacteristic
194C2×C4#1455900411yescharacteristic
195C8—41no—
196C8—6041no—
197C22#1801270711yescharacteristic
198C22#1801271611yescharacteristic
199C22#1801272511yescharacteristic
200C22SD16×D15111yescharacteristic
201C22Q16×D15111yescharacteristic
202C22#1801276611yescharacteristic
203C22#1801277111yescharacteristic
204C4—42no—
205C4—42no—
206C4—3022no—
207C4—3022no—
208C4—6042no—
209C4—12081no—
210C4#1801271611yescharacteristic
211C4#1801271811yescharacteristic
212C4#1801272511yescharacteristic
213C4#1801272611yescharacteristic
214C2#2375212411yescharacteristic
215C2#2375236111yescharacteristic
216C2#2375236611yescharacteristic
217C2#2375249511yescharacteristic
218C2#2375250511yescharacteristic
219C2#2375256111yescharacteristic
220C2#2375257311yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
FittingC2×#103×C151C2
socle, prime radicalC23×C151C2×D4
hypercenterC2×#103D151
hypocenterC151#2024
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
45. C2×Q8×C151Q8semidirect
110. C151#2024semidirect
142. C2×Q8Dic302semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#180127382
C2×#180126632
#237521192
#237519752
#237519742
#237519662
C2×#103×C1512
#2024151